EXISTENCE OF GROUNDSTATES FOR A CLASS OF NONLINEAR CHOQUARD EQUATIONS

被引：12

作者：

Moroz, Vitaly ^{[1
]}

Van Schaftingen, Jean ^{[2
]}

机构：

[1] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

[2] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain, Belgium

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 09期

关键词：

SCALAR FIELD-EQUATIONS; CRITICAL-POINTS; SYMMETRY; SYMMETRIZATION; COMPACTNESS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of a nontrivial solution u is an element of H-1(R-N) to the nonlinear Choquard equation Delta u + u = (I-alpha * F(u)) F'(u) in R-N, where I-alpha is a Riesz potential, under almost necessary conditions on the nonlinearity F in the spirit of Berestycki and Lions. This solution is a groundstate and has additional local regularity properties; if moreover F is even and monotone on (0, infinity), then u is of constant sign and radially symmetric.

引用

页码：6557 / 6579

页数：23

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